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Interference between pedestrians and motor vehicles at signalized intersections not only leads the traffic to delay and traffic efficiency to decrease, but also induces traffic crashes to happen frequently. In this paper, a microscopic discrete model for traffic flow is adopted to study the mutual interference mechanism between pedestrians and vehicles at signalized intersection. The vehicular traffic flow model is based on the refined NaSch model, and traffic lights are introduced to consider the driver anticipating in traffic signal switching. Based on the multi-step lattice gas model, the pedestrian flow model considers the fact that the pedestrians’ speed increases gradually during pedestrian cross-street green time. Both models reflect real features of movement of vehicles (pedestrians) in daily life. When the traffic light signal switches, the vehicles (pedestrians) staying in the conflict area result in the delay of pedestrians (vehicles). It is assumed that pedestrians and vehicles cannot coexist in the conflict area at the same time. In the simulation, the periodic boundary condition is applied to the lane, and the open boundary condition is applied to the crosswalk. The arrival rate of pedestrian is assumed to satisfy the Poisson distribution. Both the fundamental diagram of vehicular traffic flow and the pedestrian waiting time are calculated, and the phase diagram revealing the global nature of the presented model is obtained accordingly. The quantitative characteristics of vehicle (pedestrian) delay time caused by pedestrians (vehicles) staying in the conflict area are given as well. Simulation results show that there is a critical split. When the split is less than the critical value, three kinds of traffic phases, i.e., free flow phase, saturated flow phase, and jamming flow phase, appear with the increase of density. When the split is larger than the critical value, four kinds of traffic phases, i.e., free flow phase, coexisting phase, saturated flow phase, and jamming flow phase are distinguished. The delay caused by the mutual interference between pedestrians and motor vehicles is closely related to the state of vehicle flow and the state of pedestrian flow. When the arrival rate of pedestrians is quite large and the split is large enough, these pedestrians in the waiting area cannot be emptied once in a single pedestrian cross-street cycle. The qualitative and quantitative characteristics of mutual interference between pedestrians and vehicles are discussed in more detail. The setting of a reasonable split not only ensures the efficiency of traffic flow, but also reduces the waiting time of pedestrians to cross the street.
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Keywords:
- cellular automata /
- lattice gas model /
- pedestrian-vehicle interference /
- delay
[1] Lam W H K, Lee J Y S, Cheung C Y 2002 Transportation 29 169
Google Scholar
[2] 李文勇, 陈学武, 王庆, 李娜 2006 武汉理工大学学报 (交通科学与工程版) 30 751
Li W Y, Chen X W, Wang Q, Li N 2006 J. Wuhan Univ. Tech. (Transp. Sci. & Eng.) 30 751
[3] Guo Y Y, Sayed T, Zaki M H 2017 IET Intell. Transp. Sy. 11 28
Google Scholar
[4] Biswas S, Ghosh I, Chandra S 2017 Transp. Dev. Econ. 3 2
Google Scholar
[5] Zhang Y H, Mamun S A, Ivan J N, Ravishanker N, Haque A 2015 Accident Anal. Prev. 83 26
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[6] Ni Y, Wang M L, Sun J, Li K P 2016 Accident Anal. Prev. 96 118
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Google Scholar
[9] Li S S, Qian D L, Luo U 2012 J. Cent. South Univ. 19 3351
Google Scholar
[10] Zeng W L, Chen P, Nakamura H, Tryo-Asano M 2014 Transp. Res. C 40 143
Google Scholar
[11] Lu L L, Ren G, Wang W, Chan C Y 2015 Transp. Res. A 80 76
[12] Belbasi S, Foulaadvand M E 2008 J. Stat. Mech. 2008 P07021
[13] Myozin S 1965 T. Jpn. Soc. Civil Eng. 1965 42
[14] Xie D F, Zhao X M, Li X G 2015 Int. J. Mod. Phys. C 26 1550019
Google Scholar
[15] Zeng J W, Yu S B, Qian Y S, Wei X T, Feng X, Wang H 2017 Mod. Phys. Lett. B 31 1750238
[16] Helbing D, Jiang R, Treiber M 2005 Phys. Rev. E 72 046130
Google Scholar
[17] Muramatsu M, Irie T, Nagatani T 1999 Physica A 267 487
Google Scholar
[18] Bando M, Hasebe K, Nakayama A, Shibata A, Sugiyama Y 1995 Phys. Rev. E 51 1035
Google Scholar
[19] Nagel K, Schreckenberg M 1992 J. Phys. I (France) 2 2221
Google Scholar
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Google Scholar
[21] Barlovic R, Santen L, Schadschneider A, Schreckenberg M 1998 Eur. Phys. J. B 5 793
Google Scholar
[22] Zhang U, Duan H L, Zhang Y 2007 Tsinghua Sci. Technol. 12 214
Google Scholar
[23] Guo R Y, Guo X 2011 Chin. Phys. Lett. 28 118903
Google Scholar
[24] Xie D F, Gao Z Y, Zhao X M, Wang Z W 2012 J. Transp. Eng. 138 1442
Google Scholar
[25] Li X M, Yan X D, Li X G, Wang J F 2012 Discrete Dyn. Nat. Soc. 2012 287502
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Google Scholar
Sun Z, Jia B 2012 Acta Phys. Sin. 61 100508
Google Scholar
[27] 余艳, 白克钊, 孔令江 2013 广西师范大学学报(自然科学版) 31 6
Yu Y, Bai K Z, Kong L J 2013 J. Guangxi Normal Univ. (Nat. Sci. Ed.) 31 6
[28] Guo R Y, Lu X S 2016 J. Syst. Sci. Complex 29 202
Google Scholar
[29] Li X, Sun J Q 2016 Physica A 460 335
Google Scholar
[30] Echab H, Ez-Zahraouy H, Lakouari N 2016 Physica A 461 854
Google Scholar
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Google Scholar
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Google Scholar
Ma X L, Sun H F 2014 J. Transp. Syst. Eng. Info. Tech. 8 59
Google Scholar
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图 1 信号交叉口人-车相互作用示意图
Figure 1. Schematic diagram for vehicle-pedestrian interaction at a signalized crossing
图 2 不同绿信比下车辆运动基本图 (a)流量-密度曲线(μ = 0.5); (b)速度-密度曲线(μ = 0.5); (c)流量-密度曲线(μ = 0.9); (d)速度-密度曲线(μ = 0.9)
Figure 2. Fundamental diagrams for vehicles under different splits: (a) Flux-density relation (μ = 0.5); (b) speed-density relation (μ = 0.5); (c) flux-density relation (μ = 0.9); (d) speed-density relation (μ = 0.9).
图 3 车辆运动时空演化斑图(
$\lambda = 1.0$ ) (a) k = 0.08, μ = 0.5; (b) k = 0.40, μ = 0.5; (c) k = 0.70, μ = 0.5; (d) k = 0.15, μ = 0.9Figure 3. Temporal-spatial patterns of vehicles in motion (
$\lambda = 1.0$ ): (a) k = 0.08, μ = 0.5; (b) k = 0.40, μ = 0.5; (c) k = 0.70, μ = 0.5; (d) k = 0.15, μ = 0.9.
图 4 不同绿信比下行人等待时间随车辆密度的变化 (a) μ = 0.5; (b) μ = 0.8; (c) μ = 0.9
Figure 4. Waiting time of pedestrian varies with vehicle density under different splits: (a) μ = 0.5; (b) μ = 0.8; (c) μ = 0.9.
图 5 不同绿信比下行人等待时间随行人到达率的变化 (a) μ = 0.5; (b) μ = 0.8; (c) μ = 0.9
Figure 5. Waiting time of pedestrians varies with the arrival rate of pedestrian under different splits: (a) μ = 0.5; (b) μ = 0.8; (c) μ = 0.9.
图 6 不同绿信比时车辆所导致的行人延误 (a) μ = 0.5; (b) μ = 0.8; (c) μ = 0.9
Figure 6. Pedestrian delay time caused by vehicles under different splits: (a) μ = 0.5; (b) μ = 0.8; (c) μ = 0.9.
图 7 不同绿信比时行人造成车辆的延误 (a) μ = 0.5; (b) μ = 0.8; (c) μ = 0.9
Figure 7. Vehicle delay time caused by pedestrians under different splits: (a) μ = 0.5; (b) μ = 0.8; (c) μ = 0.9.
图 8 车流量随车辆密度和行人到达率的变化 (a) μ = 0.5; (b) μ = 0.9
Figure 8. Flux as a function of vehicle density and pedestrian arrival rate: (a) μ = 0.5; (b) μ = 0.9
图 9 行人等待时间随车辆密度和行人到达率的变化 (a) μ = 0.5; (b) μ = 0.9
Figure 9. Waiting time of pedestrian as a function of vehicle density and pedestrian arrival rate: (a) μ = 0.5; (b) μ = 0.9.
图 10 (λ, k)空间中的相图 (a) μ = 0.5; (b) μ = 0.9
Figure 10. Phase diagram in (λ, k) space: (a) μ = 0.5, (b) μ = 0.9.
表 1 各种情况下行人向邻近元胞的行走概率
Table 1. Probabilities for a pedestrian to move towards his/her neighboring cells
${S_i}$ (0, 0, 0) (1, 0, 0) (0, 0, 1) (0, 1, 0) (1, 0, 1) (0, 1, 1) (1, 1, 0) (1, 1, 1) ${p_{\rm{L}}}$ $\dfrac{{1 - p}}{3}$ 0 $\dfrac{{1 - p}}{2}$ 1/2 0 1 0 0 ${p_{\rm{F}}}$ $p + \dfrac{{1 - p}}{3}$ $p + \dfrac{{1 - p}}{2}$ $p + \dfrac{{1 - p}}{2}$ 0 1 0 0 0 ${p_{\rm{R}}}$ $\dfrac{{1 - p}}{3}$ $\dfrac{{1 - p}}{2}$ 0 1/2 0 0 1 0 
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[1] Lam W H K, Lee J Y S, Cheung C Y 2002 Transportation 29 169
Google Scholar
[2] 李文勇, 陈学武, 王庆, 李娜 2006 武汉理工大学学报 (交通科学与工程版) 30 751
Li W Y, Chen X W, Wang Q, Li N 2006 J. Wuhan Univ. Tech. (Transp. Sci. & Eng.) 30 751
[3] Guo Y Y, Sayed T, Zaki M H 2017 IET Intell. Transp. Sy. 11 28
Google Scholar
[4] Biswas S, Ghosh I, Chandra S 2017 Transp. Dev. Econ. 3 2
Google Scholar
[5] Zhang Y H, Mamun S A, Ivan J N, Ravishanker N, Haque A 2015 Accident Anal. Prev. 83 26
Google Scholar
[6] Ni Y, Wang M L, Sun J, Li K P 2016 Accident Anal. Prev. 96 118
[7] Lee J Y S, Lam W H K 2008 Transp. Res. A 42 1314
[8] Li X, Dong L Y 2012 Chin. Phys. Lett. 29 098902
Google Scholar
[9] Li S S, Qian D L, Luo U 2012 J. Cent. South Univ. 19 3351
Google Scholar
[10] Zeng W L, Chen P, Nakamura H, Tryo-Asano M 2014 Transp. Res. C 40 143
Google Scholar
[11] Lu L L, Ren G, Wang W, Chan C Y 2015 Transp. Res. A 80 76
[12] Belbasi S, Foulaadvand M E 2008 J. Stat. Mech. 2008 P07021
[13] Myozin S 1965 T. Jpn. Soc. Civil Eng. 1965 42
[14] Xie D F, Zhao X M, Li X G 2015 Int. J. Mod. Phys. C 26 1550019
Google Scholar
[15] Zeng J W, Yu S B, Qian Y S, Wei X T, Feng X, Wang H 2017 Mod. Phys. Lett. B 31 1750238
[16] Helbing D, Jiang R, Treiber M 2005 Phys. Rev. E 72 046130
Google Scholar
[17] Muramatsu M, Irie T, Nagatani T 1999 Physica A 267 487
Google Scholar
[18] Bando M, Hasebe K, Nakayama A, Shibata A, Sugiyama Y 1995 Phys. Rev. E 51 1035
Google Scholar
[19] Nagel K, Schreckenberg M 1992 J. Phys. I (France) 2 2221
Google Scholar
[20] Blue V J, Adler J L 2001 Transp. Res. B 35 293
Google Scholar
[21] Barlovic R, Santen L, Schadschneider A, Schreckenberg M 1998 Eur. Phys. J. B 5 793
Google Scholar
[22] Zhang U, Duan H L, Zhang Y 2007 Tsinghua Sci. Technol. 12 214
Google Scholar
[23] Guo R Y, Guo X 2011 Chin. Phys. Lett. 28 118903
Google Scholar
[24] Xie D F, Gao Z Y, Zhao X M, Wang Z W 2012 J. Transp. Eng. 138 1442
Google Scholar
[25] Li X M, Yan X D, Li X G, Wang J F 2012 Discrete Dyn. Nat. Soc. 2012 287502
[26] 孙泽, 贾斌 2012 物理学报 61 100508
Google Scholar
Sun Z, Jia B 2012 Acta Phys. Sin. 61 100508
Google Scholar
[27] 余艳, 白克钊, 孔令江 2013 广西师范大学学报(自然科学版) 31 6
Yu Y, Bai K Z, Kong L J 2013 J. Guangxi Normal Univ. (Nat. Sci. Ed.) 31 6
[28] Guo R Y, Lu X S 2016 J. Syst. Sci. Complex 29 202
Google Scholar
[29] Li X, Sun J Q 2016 Physica A 460 335
Google Scholar
[30] Echab H, Ez-Zahraouy H, Lakouari N 2016 Physica A 461 854
Google Scholar
[31] Deb S, Strawderman L J, Carruth D W 2018 Transp. Res. F 59 135
Google Scholar
[32] 陈然, 李翔, 董力耘 2012 物理学报 61 144502
Google Scholar
Chen R, Li X, Dong L Y 2012 Acta Phys. Sin. 61 144502
Google Scholar
[33] 马新露, 孙惠芳 2014 交通运输系统工程与信息 8 59
Google Scholar
Ma X L, Sun H F 2014 J. Transp. Syst. Eng. Info. Tech. 8 59
Google Scholar
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